20C h a p t e r 2

THE CLEAT GEOMETRY: A NOVEL RHEOLOGICAL TOOL

2.1 Wall Slip A Classical Problem with Implications in Biorheology ... 20 2.2 Materials and Methods......................................................................... 26 2.3 Quantitative Validation ......................................................................... 29 2.4 Applications in Biorheology ................................................................. 37 Bibliography ................................................................................................ 43

A significant portion of the text and figures in this chapter have been published by C. S.

Nickerson and J. A. Kornfield in the Journal of Rheology and are reproduced here with

their permission.1

2.1 Wall Slip A Classical Problem with Implications in Biorheology

Accurate rheological characterization using rheometric flows depends critically upon the

no-slip boundary condition, which essentially requires that the sample adhere to the

surfaces of the rheometer. Stated more specifically, the velocity of the sample at the sample

boundary must be equal to the velocity of the adjacent tool surface (Figure 1) so that the

deformation rate of the sample is known. Unfortunately, a wide range of materials violate

this boundary condition. For example, in suspensions and emulsions (e.g., creams, lotions,

and pastes) a thin depletion layer can form as particles/droplets migrate away from the

boundary. The depletion layer forms a planar region with reduced viscosity and so the

deformation becomes inhomogeneous. Polymers in solution are entropically driven away

from solid boundaries; in this case, depletion layers form even in the absence of flow.

21Many biological specimens slip due to the formation of lubricating layers at their

surfaces. Elastomers are susceptible to slip even without lubricating fluid layers, sliding at

the tool interface if there is insufficient friction.

Lower Plate Velocity = Vo

Sample Velocity = V(z)

V(0)=0

V(L)=Vo

Upper Plate Velocity = 0

A. No-Slip Boundary Condition

Lower Plate Velocity = Vo

Sample Velocity = V(z)

A. No-Slip Boundary ConditionUpper Plate Velocity = 0

V(0)>0

V(L)0

V(L)

22Thus, wall slip is a constant concern for rheologists working in fields ranging from

biomaterials and gels to paints and industrial products to foods and personal-care items. A

number of useful solutions to the wall-slip problem in its various forms have evolved for

specific cases.2-9 We have divided these wall-slip prevention methods into three general

approaches: mathematical methods, surface modifications, and alternative geometries

(Table 1). Each method has made important contributions to the field, but each has

significant limitations as explained below.

Approach Examples (from the literature)

Problems

MathematicalDetermine the contribution of the slip layer empirically,

then account for it

Labor intensive, Large sample requirement

Modify the Surface of Standard Fixtures

Sandpaper, Porous frit, Serrated / Grooved plates,

Chemical treatment

Not useful with thick or lubricating slip layers,

usually requires compression

Alternative Geometries Vane, Helix

Large sample volumes, Comparative (not in

absolute units), destroy delicate networks

Table 1. Existing approaches to the wall slip problem are listed with specific examples. Each approach has significant limitations as shown.

The first approach involves empirically or mathematically estimating the magnitude of the

wall slip and accounting for its contribution to rheological measurements, as explained by

Yoshimura and Prud'homme10 and Barnes.3 When possible, mathematical methods can be

23very useful because they characterize wall-slip rather than simply eliminating it.

However, mathematical methods require repetitive experiments and large sample volumes,

which can be prohibitive. Also, these methods are essentially perturbation analyses;

therefore, when slip dominates the material response, they are not applicable.

Another approach is to prevent slip by modifying the surfaces of standard rheological tools.

This is usually accomplished by either roughening the surfaces or by attaching a rough

material such as sandpaper or serrated surfaces, although chemical modifications have also

been described; examples of this are Mhetar and Archer11, Rosenberg, et al.6, and Walls, et

al.9 Surface methods have been successfully applied to systems that form thin slip layers.

Unfortunately, slip can still persist with surface modified tools in many systems,

particularly gels and elastomers. Also, to be effective in gels and solids (which includes

nearly all biological tissues), most surface-modified tools require compression or

significant normal force as described by Jin and Grodzinsky12 and Liu and Bilston13.

Typical samples are compressed a minimum of 5 10%, which can alter the structure of

the material. We observe that small compression (5%) causes the apparent modulus and

properties to increase for two biological specimens (cornea and vitreous humor) and that

delicate specimens, like the vitreous humor, are irreversibly damaged by compression of

10% or more, giving an artificial decrease in the apparent modulus.

The third approach to the wall slip problem is to use alternative geometries such as the

vaned and helical tools recently reviewed by Barnes and Nguyen2 and Cullen, et al.4, which

either prevent the formation of slip layers through mixing or measure the properties of the

sample in spite of the slip layer. The flow fields in these geometries depend upon the nature

24of the fluid; consequently, the measurements are comparative, rather than yielding

absolute modulus or viscosity values. Most alternative geometries, particularly vaned and

helical tools, are also unsuitable for delicate samples that are altered by loading into a

highly non-uniform gap.

We present a novel cleat test geometry that overcomes many of the limitations mentioned

above (Figure 2). The geometry is a modified parallel plate tool with a large number of

uniform protrusions, or cleats, extending from the faces of the plates. A key feature of the

new tool is the constant cleat length (Lc, distance from plate face to cleat tip). The

significance of uniformity is that the cleat tips create a well-defined plane within the

sample that is parallel to the plate face. Motion of fluid between the cleats is restricted and

decays to zero a short distance () into the tool. The depth at which fluid motion is stopped

establishes the effective sample gap boundary. The position of this effective sample

boundary was found to be independent of the material over the wide range of materials

examined. The penetration depth can be estimated from the geometric parameters of the

cleats and verified empirically, as will be discussed below. The only procedural difference

between cleat geometry and smooth plate experiments is the use of the effective sample

gap (gapeff = gapmeas + 2 ) rather than the measured sample gap (gapmeas).

25

gapmeas

gapeff =

gapmeas +

gapmeas

gapeff =

gapmeas +

Figure 2. Schematic representation of two cleated fixtures placed opposite each other. Sample motion penetrates only a short distance into the cleat array. The actual cleat density is high: approximately 100/cm2.

The effective sample gap is estimated by treating the array of cleats as a porous medium

and determining the flow field within it. From measurements of the in-plane, pressure-

driven flow through an array of cleats analogous to the tool, the permeability of the cleat

geometry was determined using Darcys law (k = 8.7 x 10-10 m2). Flow of Newtonian fluids

over porous media has been analyzed extensively, starting with the work of Beavers and

Joseph14 and Neale and Nader,15 who showed that the resulting motion of fluid within the

porous medium is attenuated over a short distance that is related to the permeability k (

k1/2) and is independent of the viscosity of the fluid. In highly porous media such as the

cleat geometry, Neale and Nader15 predict an exponential velocity decay profile such that

the fluid velocity in the porous region will be reduced to < 1% of the boundary velocity

when ~ 5 k1/2 (~ 150 m in the present cleat geometry). Since the attenuation depth is

26insensitive to fluid properties, the value of for Newtonian fluids provides a good

approximation for viscoelastic materials as well.

The present study demonstrates the accuracy and utility of the cleat geometry. We show

that this unique geometry for slip prevention accommodates small sample volumes and

allows direct measurement of shear modulus using a gentle loading procedure and

negligible normal force. Results obtained with the cleated tools are compared with those

obtained using smooth and roughened parallel plate geometries. First, for fluids that do not

exhibit slip, the results confirm that quantitative measurements can be obtained using a

single value of the gap correction . The empirical value for based on these fluids is

compared with k1/2 to evaluate the applicability of the porous medium analogy. Next we

show that the tool performs well when applied to two fluids that exhibit moderate slip, and

we validate the results independently using roughened plates. Finally, the power of the new

geometry is illustrated by obtaining modulus measurements for porcine cornea and vitreous

humor, two biological tissues that are difficult or impossible to handle successfully with

prior tools. More comprehensive rheological characterization of cornea and vitreous tissue

will be presented in conjunction with chemical analysis in subsequent chapters.

2.2 Methods and Materials

Four different tools were used to measure the shear moduli and viscosities of a variety of

materials, from low viscosity Newtonian oils to slippery biological tissues. The primary

reference tool was a smooth 25 mm titanium parallel plate test geometry. A rough tool was

made by attaching fine emery cloth to the surface of a 25 mm aluminum parallel plate

27geometry. Two of the cleated tools were likewise 25 mm in diameter. Cleats were

machined into an aluminum disk, leaving protrusions with a square cross section 0.45 mm

x 0.45 mm, evenly spaced 1.35 mm apart (center to center). Two Lc values were used: 0.6

mm and 1.3 mm. A second set of smooth, rough, and cleated tools with 0.6 mm cleats and

8 mm diameters were used for measurements on cornea. In addition, a vaned fixture and

porous plates were used when roughened plates failed (on vitreous humor), but they were

unsatisfactory. The 25 mm tools were mounted on an ARES-RFS fluids rheometer, while

the 8 mm tools were mounted on an AR2000 rheometer (both from T.A. Instruments, Inc.,

New Castle, DE) with sample gaps ranging from 2.25 mm to 0.3 mm. The in-plane

permeability of the cleated tools was measured by Porous Materials, Inc. (Ithaca, NY).

Four of the test fluids were selected specifically because they are not prone to slip: a series

of three silicone oils, ( = 10, 1.0, and 0.1 Pas respectively) and GE Silicones SE-30

polydimethylsiloxane (PDMS) putty (Waterford, NY). The 10 Pas fluid was methyl

silicone oil purchased from Nye Lubricants, Inc. (New Bedford, MA); the 1.0 and 0.1 Pas

oils were silicone viscosity standards from Brookfield Engineering Laboratories, Inc.

(Middleboro, MA). In experiments on these fluids the upper tool was cleated and the lower

surface was smooth. Using a smooth lower plate allowed us to validate the cleats at large

sample gaps with low viscosity fluids. Each fluid was tested at least three times per sample

gap at 22 C and multiple shear rates (1 80 s-1) or frequencies (10-1 102 rad/s); the

PDMS putty was tested in the linear viscoelastic regime ( = 0.2%).

To demonstrate the utility of the cleated geometry for samples that slip, two food products

and two biological tissues were characterized using smooth, rough, and cleated tools (both

28upper and lower fixtures). The foods used were Kroger brand Real Mayonnaise

(Kroger Co., Cincinnati, OH), an oil in water emulsion, and Winn-Dixie brand Creamy

Peanut Butter (Winn-Dixie Stores, Inc., Jacksonville, FL), a suspension, both of which

exhibit slip on smooth tools. Samples were tested at least three times at 5 C and multiple

shear rates (10-2 10 s-1). The biological tissues were fresh porcine eyes (< 36 hours post

mortem, stored at 5 C in physiological saline prior to arrival) were acquired through Sierra

for Medical Science (Santa Fe Springs, CA). All pigs were 3 6 month old Chester

Whites, weighing 50 100 kg and in good health at the time of slaughter. Cornea is a slip-

prone biological elastomer with a complex network structure, as will be discussed in

subsequent chapters. The vitreous humor is an example of a delicate hydrogel that exhibits

slip even on rough tools. Eyes from 3 6 month old swine were enucleated immediately

after the animals were sacrificed and shipped at ~ 5 C in physiological saline. Fresh eyes

were gently dissected between 24 and 36 hours post mortem (no cornea or vitreous

degradation is seen within ~ 48 hours when the eye is maintained in Dulbeccos phosphate

buffered saline at 5 C), and the vitreous was removed with minimal disruption, leaving the

cornea for parallel analysis. From the intact vitreous, a disc-like section approximately 25

mm in diameter was cut with the axis of the disc coinciding with the anterior-to-posterior

axis of the eye (typically 1.5 2.5 g). 8 mm discs were cut from the central cornea (n 4

for each tool). To mitigate the effects of drying, a vapor trap was used in all experiments.

Vitreous time-dependent shear modulus measurements were made at 20 C with zero

normal force on the samples at a fixed strain and frequency ( = 3%, = 10 rad/s), while

variable stress, fixed frequency cornea (5 C) measurements were made at = 1 30 Pa,

29= 1 rad/s. More extensive rheological analysis of these materials will be presented in

subsequent chapters.

2.3 Quantitative Validation

Newtonian Oils: The viscosities of three silicone oils were measured with the smooth

parallel plate geometry and with one of the parallel plates replaced by a cleated tool. Two

different cleat lengths (600 m and 1300 m) were compared. At least four different

sample gap values were tested for each tool configuration. For smooth tools, the measured

viscosity is independent of gap (Figure 3). The viscosity obtained with cleated tools is

insensitive to gap thickness when gapmeas 1 mm, indicating

30

Figure 3. The viscosity of three Newtonian oils was measured at multiple gaps with two cleated tools and compared with measurements made with a smooth titanium plate. At small gaps cleat geometry values diverge from smooth plate values.

Experimentally-determined correction values also compare favorably with predictions.

Based on the porous-medium analogy, the gap-dependent disparity between viscosity

measurements from smooth (true) and cleated tools (meas) is predicted to be:

( )

+= measmeas

true

measgap

gap

Note that would be replaced by 2 if both faces were cleated rather than just the upper

tool. This expression accords well with the experimental results as a function of gap

31(Figure 4). A single value of holds for all three Newtonian oils. Non-linear least

squares fitting of true

meas

to 1

1

+

measgap yields an empirical value of = 157 m

(95% CI = 141 173 m), in remarkably good agreement with the predicted value above.

Application of the 157 m correction factor to the Newtonian oil data (Figure 3)

demonstrates the accuracy of Figure 5.

Figure 4. Viscosity measured using the cleat geometry divided by true viscosity, measured by the smooth plates. The solid curve shows the predicted gap dependence (1+ / gapmeas)-1 with a value of = 157 m. Dashed curves bound the 95% confidence interval (141 m < < 173 m).

32

Figure 5. The cleat geometry viscosity data from Figure 3 plotted after gap correction with = 150 m. Accurate measurements are obtained at all gaps and viscosities when the gap is accounted for correctly.

PDMS Putty: The uncorrected storage and loss moduli of PDMS putty (o > 104 Pa s)

measured with the two cleated tools were consistently lower than those measured using the

smooth parallel plates; however, the 157 m correction factor brings the cleat

measurements within 1% of the parallel plate results (Figure 6). G and G measurements

were accurate over the three decades of frequency examined, and the gap dependence

matched that of the Newtonian oils. Thus, appears to be independent of material

33properties for a wide range of soft materials and fluids, including a complex fluid, as

anticipated from the porous medium analogy.

Figure 6. Gap corrected shear moduli of PDMS putty measured with the cleat geometry are within 1% of values obtained using a titanium parallel plate over three decades of frequency and modulus ( = 0.2%, gapmeas = 2 mm).

The experimental results for Newtonian oils support our hypothesis that the cleats create an

effective no-slip boundary that is close to the plane of the cleat tips. Furthermore, the

observation that the ratio of the apparent viscosity observed using cleated tools, meas, to

actual viscosity, true, is independent of the viscosity of the fluid accords with a model that

34treats the array of cleats as a porous medium. The attenuation distance = 157 m

inferred from the ratio of true

meas

is similar to 5 k1/2 determined independently. The

experimental observation that the correction factor determined for a series of Newtonian

fluids also applies for a viscoelastic fluid (an entangled polymer melt, Figure 6) over a

frequency range that spans from near terminal behavior (G < G) to elastic behavior (G >

G) suggests that the attenuation depth continues to be governed by the geometry of the

cleat array even for some non-Newtonian fluids.

The gap dependence of meas is reminiscent of slip phenomena; however, the fluid

independence of the value, combined with the improbability of slip with the samples

chosen, demonstrate that represents a true sample gap boundarynot a slip length. The

cleat geometry creates a secondary boundary at a distance below the cleat tips where the

no-slip condition effectively holds. The dependence 1

1

+=

meastrue

measgap

corresponds to the apparent gap effect noted by Sanchez-Reyes and Archer.8 We have

shown that an empirical can be inferred that appears to be accurate for the samples

investigated and is consistent with the observed dependence of meas on gapmeas down to the

smallest gap tested (gapmeas 2 ).

Optimization of the cleat parameters (height, width, length, and spacing) involves a trade

off between minimizing the attenuation length and minimizing the disruption of the sample.

Therefore, one can decrease by reducing k through an increase in the area of the cleated

surfaces per unit area of the tool. However, increasing the cross-section of each cleat or the

35cleat surface density hinders penetration into samples such as gels, elastomers, and

biological tissue. The specific parameters of the cleat array we describe have the advantage

that only 11% of the nominal surface area (area relevant to penetration) of the disk is

occupied by the cleats themselves. This arrangement of well-spaced pins readily

penetrates diverse complex fluids and certain soft solids. As stated previously, the

permeability k of the cleat arrangement determines , which subsequently dictates the

minimum value of Lc. Based on the findings of Sanchez-Reyes and Archer, the optimal

length scale of the surface features will decrease as the modulus range of interest

increases.8 They observed that with increasing polymer concentration, i.e., decreasing size

of entangled blobs, the optimal sizes of surface features decreases.

Peanut Butter and Mayonnaise: To validate that the cleat geometry is also accurate in

moderately slip-prone systems, we compare results obtained for a model suspension and a

model emulsion to results obtained using published methods. The viscosity of peanut butter

(Figure 7) and mayonnaise (Figure 8) were measured using smooth, rough, and cleated

tools at gapmeas = 2 mm. Prior literature, including work by Citerne, et al.16 and Franco, et

al.17, shows that roughened plates are adequate to suppress slip for both of these complex

fluids. Peanut butter, a typical suspension, and mayonnaise, an oil-in-water emulsion, both

exhibit slip at low shear rates on smooth plates, giving apparent values of considerably

smaller than values measured with rough plates. The measured viscosity of both samples

was essentially the same with cleated or roughened plates. Apparently, the characteristic

feature sizes of both tools were larger than the thin depletion layers that cause slip. On a

practical note, it was observed that, relative to emery cloth and porous glass, the cleated

36tools were far easier to clean and more robust against physical damage, solvents, and

high temperatures.

Figure 7. The corrected viscosity of peanut butter measured with cleated and rough plates. Smooth plates show slip at low shear rates (gapmeas = 2 mm).

37

Figure 8. The corrected viscosity of mayonnaise measured with cleated and rough plates. Smooth plates show slip at low shear rates (gapmeas = 2 mm).

2.4 Applications in Biorheology

Cornea: Results obtained from cornea specimens demonstrate the utility of the cleat

geometry for soft elastomeric materials. Corneal tissue is a valuable example in this regard

because it can be characterized on smooth tools for comparison with results obtained in

cleated tools. Immediately after dissection, corneal tissue is slippery and remains so even

after the epithelial cell layer is removed. Fortunately, if the surfaces are briefly put in

contact with an absorbent material, the surface is no longer slippery. There is negligible

weight change (< 3%) in the process, so the viscoelastic properties of the tissue closely

approximate the tissue in vivo. Thus, we regard results from the smooth tools as an accurate

reference against which other tool surfaces can be compared. Gap-corrected shear modulus

38measurements from the cleat geometry agree quantitatively with measurements obtained

with smooth tools (Figure 9). The standard deviation (for n = 4) is, unfortunately, much

greater on cleated tools than on smooth tools. This suggests a direction for future research:

evaluation of the effect of cleat size relative to tool size. For example, on an 8 mm tool

there are only 35 40 cleats, so that from one sample loading to the next, details of loading

and azimuthal orientation of tools could lead to significant variations.

Figure 9. Gap corrected shear modulus of fresh porcine cornea at fixed frequency (w = 1 rad/s) and 5 C using smooth, roughened, and cleated tools. Tools were lowered until ~ 0.1 N of normal force was detected, then the sample was allowed to relax completely and tested (n = 4).

39Values obtained with roughened tools are systematically too low (Figure 9). This

comparison is made using the same normal force in all three cases, with a normal force

small enough that the tissue is not damaged. Cornea samples were loaded by slowly

lowering the upper fixture until the normal force was ~ 0.1 N. The normal force decayed to

zero within seconds. Small amplitude oscillatory shear was used to observe relaxation of

the sample to a steady state (~ 15 minutes was sufficient) and then measurements were

made. This loading technique was sufficient to generate good contact between the smooth

tool and the cornea and to allow adequate penetration by the cleats. However, in accord

with prior literature, such low normal force is insufficient to allow the irregular surface

features of the roughened tool to fully grip the sample. This demonstrates a significant

advantage of the cleats over roughened tools adequate measurements can be made using

negligible normal force.

Vitreous Humor: Results obtained from the vitreous humor of the eye demonstrate the

utility of the cleat geometry for more difficult samples. Previous efforts to measure the

mechanical properties of the vitreous, including work by Bettelheim and Wang,18 Lee, et

al.,19 Pfeiffer,20 Tokita, et al.,21 and Zimmerman,22 have yielded unsatisfactory and

sometimes conflicting results. The shear moduli of this delicate tissue were also impossible

to measure using previously published geometries in our laboratory (Figure 10). Smooth

plates slipped drastically, and roughened plates were insufficient because slip was not

consistently prevented (as denoted by the large standard deviation). While some vitreous

samples appeared to be measured accurately on the rough fixtures, other loadings appeared

to fail (slip) from the first data point, yielding results similar to those obtained with the

40smooth tools. The normal force required to obtain measurements with roughened tools

artificially raised the apparent modulus in the initial data points. Over the course of a

typical experiment, the apparent modulus decreased with the normal force as fluid was

squeezed out of the tissue. In conjunction with fluid loss, a thick lubricating layer formed

within five minutes, making it impossible to eliminate slip using roughened plates. In

previous efforts to measure the modulus of the vitreous, the use of porous plates failed for

the same reasons as roughened plates. The vane geometry was unsuitable because it

destroyed the gel network and sample volume is limited to the size of a single eye.

Figure 10. The corrected shear modulus of freshly-enucleated vitreous humor measured with the cleat geometry is far more consistent than rough plates and clearly more accurate than smooth plates (g = 3%, w = 10 rad/s, n = 9).

41Using the cleat geometry, these obstacles appear to have been overcome and consistent

shear moduli were measured. The modulus values measured with the cleat geometry are

slightly greater than those obtained with roughened tools, but the most obvious

improvement is the reduction in standard deviation (Figure 10). Comparing results obtained

using the cleat geometry with literature values obtained using other methods suggests that

the shear moduli of the vitreous are significantly higher than reported in the works

mentioned above. The cleat geometry has also allowed us to quantify time-dependent

modulus changes that were previously reported only as qualitative observations.

Results from the vitreous humor demonstrate some advantages of the cleat geometry.

Highly-charged hyaluronic acid (HA), which draws water into the vitreous in vivo, seeps

out of the vitreous when it is removed from the eye. The HA solution that blooms to the

surface is a very efficient lubricant, similar to the synovial fluid that lubricates the joints.

This HA solution causes the wall slip observed even on very rough surfaces such as

sandpaper and porous plates. Note that the successful modeling of cleats as porous media

does not imply that porous surfaces work as well as cleats: they do not. The advantage of

using cleats over standard porous materials such as fritted disks is that the cleats protrude

orthogonally from the tool face and engage the sample.

There is an important, transient decrease in modulus that occurs spontaneously after the

vitreous is removed from the eye, captured in measurements using the cleat geometry. It is

not possible to characterize this transient behavior using roughened plates due to the need

to apply a substantial normal force; the strong effects of compression mask the natural

decay. Thus, the cleat geometry is uniquely capable of measuring the time-dependent

42changes in this sample, which is too slippery and fragile to be measured accurately using

previously published methods. Because prior mechanical investigations of the vitreous are

unsatisfactory, we have no way to independently verify the accuracy of our modulus

values. The sample dictates the gap and is destroyed by compression; therefore, the usual

procedure to test for slip (varying sample geometry) cannot be applied. The values we

report represent a lower bound: potential sources of error in the cleat geometry (wall slip,

insufficient surface contact, or increased flow between the cleats) would reduce the

apparent modulus. We observed that near the tools heterogeneities in the tissue moved with

the tool surface; therefore, we believe that the above errors are small.

The modulus values here pertain to the central vitreous, the bulk of the tissue. The work of

Lee, et al. suggests that different moduli would characterize the tissue near the anterior pole

(stiffer).19 Regional variations in tissue properties will be discussed in conjunction with

more complete rheological and structural analyses presented in subsequent chapters.

43BIBLIOGRAPHY

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2. Barnes HA, Nguyen QD. Rotating vane rheometry - a review. Journal of Non-Newtonian Fluid Mechanics. Mar 15 2001;98(1):1-14.

3. Barnes HA. A Review of the Slip (Wall Depletion) of Polymer-Solutions, Emulsions and Particle Suspensions in Viscometers - Its Cause, Character, and Cure. Journal of Non-Newtonian Fluid Mechanics. Mar 1995;56(3):221-251.

4. Cullen PJ, O'Donnell CP, Houska M. Rotational rheometry using complex geometries - A review. Journal of Texture Studies. Apr 2003;34(1):1-20.

5. Klein B, Laskowski JS, Partridge SJ. A New Viscometer for Rheological Measurements on Settling Suspensions. Journal of Rheology. Sep-Oct 1995;39(5):827-840.

6. Rosenberg M, Wang Z, Chuang SL, Shoemaker CF. Viscoelastic Property Changes in Cheddar Cheese During Ripening. J. Food Sci. MAY-JUN 1995 1995;60(3):640-644.

7. Russel JL. Studies of thixotropic gelation. Part II. The coagulation of clay suspensions. Proc. Roy. Soc. London, Series A. 1936;154:550-560.

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9. Walls HJ, Caines SB, Sanchez AM, Khan SA. Yield stress and wall slip phenomena in colloidal silica gels. Journal of Rheology. Jul-Aug 2003;47(4):847-868.

10. Yoshimura A, Prud'homme RK. Wall Slip Corrections for Couette and Parallel Disk Viscometers. Journal of Rheology. JAN 1988 1988;32(1):53-67.

11. Mhetar V, Archer LA. Slip in entangled polymer melts. 2. Effect of surface treatment. Macromolecules. Dec 1 1998;31(24):8617-8622.

12. Jin MS, Grodzinsky AJ. Effect of electrostatic interactions between glycosaminoglycans on the shear stiffness of cartilage: A molecular model and experiments. Macromolecules. Nov 6 2001;34(23):8330-8339.

13. Liu Z, Bilston L. On the viscoelastic character of liver tissue: experiments and modelling of the linear behaviour. Biorheology. 2000;37(3):191-201.

14. Beavers GS, Joseph DD. Boundary Conditions At A Naturally Permeable Wall. Journal Of Fluid Mechanics. 1967;30:197-207.

15. Neale G, Nader W. Practical Significance of Brinkman's Extension of Darcy's Law: Coupled Parallel Flows within a channel and a Bounding Porous Medium. Can. J. Chem. Eng. August 1974 1974;52:475-478.

16. Citerne GP, Carreau PJ, Moan M. Rheological properties of peanut butter. Rheol. Acta. JAN 2001 2001;40(1):86-96.

17. Franco JM, Gallegos C, Barnes HA. On slip effects in steady-state flow measurements of oil-in- water food emulsions. Journal of Food Engineering. Apr 1998;36(1):89-102.

4418. Bettelheim FA, Wang TJY. Dynamic Viscoelastic Properties of Bovine

Vitreous. Experimental Eye Research. 1976;23(4):435-441. 19. Lee B, Litt M, Buchsbaum G. Rheology of the vitreous body: Part 2.

Viscoelasticity of bovine and porcine vitreous. Biorheology. Jul-Aug 1994;31(4):327-338.

20. Pfeiffer HH. Zur analyse der fliess-elastizitaet durch spinnversuche am corpus vitreus. Biorheology. 1963;1:111-117.

21. Tokita M, Fujiya Y, Hikichi K. Dynamic viscoelasticity of bovine vitreous body. Biorheology. 1984;21(6):751-756.

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